基于分形理论及图像纹理分析的水稻产量预测方法研究
摘要
估产是精确农业领域的一个重要研究内容,目前,国内外相关方面的研究报导很多,有的估产方法已达到实际应用阶段。但在目前的众多估产方法中,有的方法存在人力、物力投入过大的不足,有的方法存在基础数据收集复杂的不足,使估产方法难于在农村基层组织推广使用。所以研究简单、实用、投入相对较少的产量精确预测方法意义重大。
本文在分析现有估产方法的基础上,提出了基于纹理分析、分形理论建立水稻产量精确预测数学模型的研究思路及实验方案。目前产量测量方法主要分为：传统的田间实地抽样调查法,遥感估产和作物环境模型。传统的田间实地抽样方法费时、费力,效率低下；作物环境模型中的气象预报模型和农学预报模型需要大量的气象资料和农学特征参数,存在模型资料获取难度较大的问题。分形理论和纹理分析方法对于解决具有微观上杂乱无序,但宏观上有序的物体具有明显优势。因此本研究基于分形理论和图像纹理分析方法,以成熟期水稻作为主要研究对象,结合图像处理技术,用数学统计理论建立水稻穗头、田间平方米产量的数学模型,为实现田间精确预测产量解决了关键技术。主要研究内容和取得的结论归纳如下：
1、提出了一个全新的产量预测思路与实现方法。在总结了目前产量预测方法的优点与不足后,提出了以成熟期水稻图像为主要研究对象,通过对图像进行分析、处理,来预测产量。这一思路,在目前产量预测方法的研究方面是个全新的思路。这种产量预测方法实现了方法简单、实用、投入较少的目的,为今后进一步研究田间产量精确预测系统奠定理论基础；
2、提取水稻穗头、田间群体图像的分形特征参数。水稻穗头与水稻群体在局部区域内呈现明显的不规则性,在传统的欧氏几何范畴来研究解决其本身特性参数的提取难度比较大,分形理论的应用则为提取水稻穗头、水稻群体图像特征参数的提取提供了一种极为有效的途径。本文根据分形的几何特征研究水稻穗头、田间水稻群体图像是否具有分形特征；根据分形维数的定义和现有分形维数的计算原理,研究分形维的提取算法,基于VC++平台开发编写分形维提取程序,有效提取经过图像预处理过的水稻穗头、田间水稻群体图像的分形维。研究结果：水稻穗头、田间群体图像具有分形特性；编制了适于提取二值图的计盒维数(Box Counting)的程序、适于提取灰度图的差分计盒维数(Differential Box Counting)和多重分形维计算程序；利用自编程序提取了水稻穗头图片的计盒维数(BC)和差分计盒维数(DBC)；还提取了田间水稻平方米群体图像的差分计盒维数(DBC)和多重分形维指数图(q-D(q)图)；
3、提取水稻穗头、田间群体图像的纹理特征参数值。水稻穗头和水稻群体图像在局部区域内呈现不规则性,在整体上表现出某种规律性,这是典型的纹理特性。本文根据纹理特征的常用描述、统计方法,编制了基于灰度图像直方图纹理统计原理的一次统计量纹理特征提取程序；提取了基于直方图特征(一次统计量)的纹理统计量：灰度均值、方差、平滑度、三阶矩、一致性、熵；提取了基于灰度共生矩阵(二次统计量)的纹理统计量：角二阶矩、相关度、对比度、熵、逆差矩、和方差；还提取了基于灰度梯度共生矩阵(二次统计量)的纹理统计量：能量、灰度不均匀度、梯度不均匀度、相关度、混合熵、惯性、逆差矩；
4、研究提取的水稻穗头、田间水稻群体图像分维、纹理特征参数值与水稻穗头质量、田间平方米产量的相关关系。结果表明：与穗头质量存在线性相关关系的穗头图像特征参数为：计盒维数、差分计盒维数、直方图统计的纹理特征值(均值、标准差、平滑度、三阶距、一致性、熵)、灰度共生矩阵的相关度和对比度、灰度梯度共生矩阵的灰度不均匀度和梯度不均匀度；与水稻平方米产量存在线性相关关系的水稻群体图像特征参数为：差分计盒维数、多重分形维D(5)(5是多重分形分析时的指数值)、直方图统计的熵、灰度共生矩阵的对比度、灰度梯度共生矩阵的灰度不均匀度、梯度不均匀度；
5、对提取的特征参数进行主成分分析,将与产量具有相关关系的多个参数化为少数几个综合指标。为了能全面、系统地找出表征产量的特征参数,考虑了众多影响水稻穗头,水稻单位面积产量的因素。这些因素从个体来说,都与产量有相关关系,但可能存在信息冗余,重复表述的问题,并且变量太多增加分析问题的难度与复杂性,所以采用主成分分析方法对所有变量进行筛选,从中选取若干对产量具有最佳解释能力的新综合变量。结果表明：对与水稻穗头质量相关性比较显著的特征参数作主成分分析后,确定贡献率高达99.02%的第一主成分代替原先的14个特征参数作为新的综合变量；对水稻群体平方米产量的特征参数作主成分分析后,确定了累计贡献率达99.95%的第一、第二主成分代替原来的7个特征参数作为新的综合变量；
6、用多元线性回归方法建立水稻穗头质量、水稻平方米产量的数学模型。建立的穗头质量模型为:Y=5.7174-0.3668z1,式中Y为穗头质量,Z1为表征穗头质量的主成分；建立水稻平方米产量模型为：Y=0.7889+0.0598z1+0.0295z2+0.0541z3,式中Y为每平方米产量,单位kg/m2,Z1、Z2、Z3是水稻平方米产量的主成分。
7、用后验差检验法对模型精度进行验证。后验差检验验证残差分布的统计特性,验证结果为：穗头质量模型精度为一级——优,田间平方米产量的模型精度为三级——勉强合格。
本研究为分形理论、纹理分析在农业工程方面的应用提供一种新的思路和启发。水稻穗头质量模型的建立将为水稻品种的培育研究提供参考依据；平方米水稻产量模型的建立将为水稻产量测量提供一种新的方法,为联合收割机的测产装置提供一种新的选择。
Pre-estimating the yield of grain crops is one of the significant content of the precision agriculture. Currently, many relevant researches have been reported over the world, and so(?)ne pre-estimating approaches have been applied to the practical production. However, most of these methods have the disadvantages of needing many manpower as well as material recourses, and some of them were very unconvinent in collecting basic data, thus it is too difficult to popularize these methods in rural area. Simple, practical and less-investment methods for pre-estimating the yield have been required.
In this paper, author proposed a novel method for estimating the paddy yield on the basis of the fractal theory and the image texture analysis. Presently, traditional on-the-spot sampling and survey methods, remote sensing yield estimating and predicting yield based on the crop-environment model are three main methods. Traditional on-the-spot sampling and survey methods are time and labor consuming and low efficiency. Remote sensing yield estimating needs an enormous input of finacial and material recourses. For the methods based on the crop-environment model, it is very hard to collect the vast amount of meteorological data and agricultural feature parameters. The image texture analysis and the fractal theory have the superiority in describing objects which present abnormities in a microscopic scales but show regularities in a macroscopic scales. In this paper, based on image texture analysis and the fractal theory, feature parameters of mass were extracted from images of individual paddy spikes and paddy plots, the correlativities between these feature parameters and the yields were studied, mathematical models were established to measure the mass of individual paddy spikes and the per-square-meter yields of paddy plots. Finally,the PCA technology was used for precision pre-estimating the yield of grain crops. Main contents and conclusions were summed up as follows:
1. A novel thought and approach was brought foreward for pre-estimating the yield of paddy crops. In this paper, based on the images of individual paddy spikes and paddy plots in their maturation phase, using digital image processing technology, and combining with the fractal theory and the texture analysis, a new method was designed and studied to estimate the yield of paddy grain. This method achieved the aim of simple, practical and less-investment, and provided a theoretical basis for further researches about accurate yield pre-estimating system.
2. Fractal feature parameters of the images of paddy spikes and paddy plots were extracted. The shap of individual paddy spikes and paddy plots present an distinct abnormity in partial areas. Obviously, it is very hard to derive characteristic parameters in a traditional domain of Euclidean geometry. The fractal theory provides us a effective way to extract feature parameters of the images of paddy spikes and paddy plots. In this paper, whether those images bear fractal features were studied, the algorithms of extracting the fractal demention (FD) were worked over based on the definition and the existing calculating principles of the FD, and eventually the FDs were extracted from preprocessed images of paddy spikes and paddy plots using a calculation programme exploited on a VC++ platform. The result shows that the images of paddy spikes and paddy plots bear fractal features. In our researches, calculation programmes were disigned to extract the Box Counting Dimensions (BC) from binorized images, the Differential Box Counting Dimensions (DBC) and the multi-fractal dimensions (D(5)), and relevent feature parameters were extracted.
3. Texture feature parameters of the images of paddy spikes and paddy plots were extracted. The texture of individual paddy spikes and paddy plots present an abnormity in partial areas, but as a whole, it shows a certain regularity. This is the characteristic of the texture. In this paper, based on the description and the statistical methods of texture feature, calculation programmes were designed to extract textural feature parameters. From histogram features, the mean, the variance, the smoothness, the consistency, the third order moment and the entrop of the gray level were extracted. From the gray-level co-occurrence matrix, the diagonal second order moment, the correlation degree, the contrast grade, the entrop, the inverse difference moment and the variance of sum were extracted. And from the gray level-gradient co-occurrence matrix, the energy, the gray average, the gradient average, the correlation degree, the entropy of mixing, the inertia and the inverse difference moment were extracted.
4. The correlativity between the different Box-Counting Dimensions and the textual feature parameters of the images of paddy spikes and paddy plots and the masses of paddy spikes and the per-square-meter yield of paddy plots studied. The result shows that feature parameters which have linear correlativity with the masses of paddy spiked are BC, DBC, texture feature parameters extracted from histogram features (the mean, the variance, the smoothness, the third order moment, the consistency and the entrop of the gray level), the correlation degree and the contrast grade extracted from the gray-level co-occurrence matrix, and thegray average, the gradient average of the gray level-gradient co-occurrence matrix, and those have linear correlativity with the per-square-meter yield of paddy plots are DBC, D(5), the entropy of histogram features, the contrast grade of the gray-level co-occurrence matrix, the gray average and the gradient average of the gray level-gradient co-occurrence matrix.
5. In our research, Principal Component Analysis (PCA, a vector space transform often used to reduce multidimensional data sets to lower dimensions for analysis) were used to extract some aggregate variables which bear best explanatory ability to the yield. Instead of the original variables, fewer new aggregate variables were used in establishing regression models. These models were used to forecast the mass of individual paddy spike and the per-square-meter yields. The result shows that, instead of primary 7 feature parameters, the contribute rate of the first principal component is as high as 92.83%. instead of primary 6 feature parameters, the contribute rate of the first and the second principal components is as high as 97.37%.
6. The multiple linear regression equation method were used in establishing mathematical models for measuring the masses of individual paddy spikes and the per-square-meter yields of paddy plots. The model for measuring the masses of individual paddy spikes could described as:Y=5.7174-0.3668z,, where Y equals the mass of a paddy spike, Z1 equals the principal components. The model for measuring the per-square-meter yields could described as:Y=0.7889+0.0598z1+0.0295z2+0.0541z3, where Y equals the per-square-meter yield, Z1, Z2, Z2 equals the first and the second principal components.
7. The posterior-variance-test was used in model precision grade testing. Results show that the precision grade of the model for measuring the masses of individual paddy spikes isⅠ(excellent). The precision grade of the model for measuring the per-square-meter yields isⅢ(reluctantly qualified).
This research provided a novel idea and inspiration for the application of the fractal theoty and the image texture analysis in agricultural engineering. The model, which was used to measure the mass of individual paddy spike, would give references to the researches of cultivating new paddy varieties. The models of the per-square-meter yield provide a novel approach to measuring the yields of paddy rice, and could give a new choice in designing an estimating device which could be fixed on a combine harvester.
本文在分析现有估产方法的基础上,提出了基于纹理分析、分形理论建立水稻产量精确预测数学模型的研究思路及实验方案。目前产量测量方法主要分为：传统的田间实地抽样调查法,遥感估产和作物环境模型。传统的田间实地抽样方法费时、费力,效率低下；作物环境模型中的气象预报模型和农学预报模型需要大量的气象资料和农学特征参数,存在模型资料获取难度较大的问题。分形理论和纹理分析方法对于解决具有微观上杂乱无序,但宏观上有序的物体具有明显优势。因此本研究基于分形理论和图像纹理分析方法,以成熟期水稻作为主要研究对象,结合图像处理技术,用数学统计理论建立水稻穗头、田间平方米产量的数学模型,为实现田间精确预测产量解决了关键技术。主要研究内容和取得的结论归纳如下：
1、提出了一个全新的产量预测思路与实现方法。在总结了目前产量预测方法的优点与不足后,提出了以成熟期水稻图像为主要研究对象,通过对图像进行分析、处理,来预测产量。这一思路,在目前产量预测方法的研究方面是个全新的思路。这种产量预测方法实现了方法简单、实用、投入较少的目的,为今后进一步研究田间产量精确预测系统奠定理论基础；
2、提取水稻穗头、田间群体图像的分形特征参数。水稻穗头与水稻群体在局部区域内呈现明显的不规则性,在传统的欧氏几何范畴来研究解决其本身特性参数的提取难度比较大,分形理论的应用则为提取水稻穗头、水稻群体图像特征参数的提取提供了一种极为有效的途径。本文根据分形的几何特征研究水稻穗头、田间水稻群体图像是否具有分形特征；根据分形维数的定义和现有分形维数的计算原理,研究分形维的提取算法,基于VC++平台开发编写分形维提取程序,有效提取经过图像预处理过的水稻穗头、田间水稻群体图像的分形维。研究结果：水稻穗头、田间群体图像具有分形特性；编制了适于提取二值图的计盒维数(Box Counting)的程序、适于提取灰度图的差分计盒维数(Differential Box Counting)和多重分形维计算程序；利用自编程序提取了水稻穗头图片的计盒维数(BC)和差分计盒维数(DBC)；还提取了田间水稻平方米群体图像的差分计盒维数(DBC)和多重分形维指数图(q-D(q)图)；
3、提取水稻穗头、田间群体图像的纹理特征参数值。水稻穗头和水稻群体图像在局部区域内呈现不规则性,在整体上表现出某种规律性,这是典型的纹理特性。本文根据纹理特征的常用描述、统计方法,编制了基于灰度图像直方图纹理统计原理的一次统计量纹理特征提取程序；提取了基于直方图特征(一次统计量)的纹理统计量：灰度均值、方差、平滑度、三阶矩、一致性、熵；提取了基于灰度共生矩阵(二次统计量)的纹理统计量：角二阶矩、相关度、对比度、熵、逆差矩、和方差；还提取了基于灰度梯度共生矩阵(二次统计量)的纹理统计量：能量、灰度不均匀度、梯度不均匀度、相关度、混合熵、惯性、逆差矩；
4、研究提取的水稻穗头、田间水稻群体图像分维、纹理特征参数值与水稻穗头质量、田间平方米产量的相关关系。结果表明：与穗头质量存在线性相关关系的穗头图像特征参数为：计盒维数、差分计盒维数、直方图统计的纹理特征值(均值、标准差、平滑度、三阶距、一致性、熵)、灰度共生矩阵的相关度和对比度、灰度梯度共生矩阵的灰度不均匀度和梯度不均匀度；与水稻平方米产量存在线性相关关系的水稻群体图像特征参数为：差分计盒维数、多重分形维D(5)(5是多重分形分析时的指数值)、直方图统计的熵、灰度共生矩阵的对比度、灰度梯度共生矩阵的灰度不均匀度、梯度不均匀度；
5、对提取的特征参数进行主成分分析,将与产量具有相关关系的多个参数化为少数几个综合指标。为了能全面、系统地找出表征产量的特征参数,考虑了众多影响水稻穗头,水稻单位面积产量的因素。这些因素从个体来说,都与产量有相关关系,但可能存在信息冗余,重复表述的问题,并且变量太多增加分析问题的难度与复杂性,所以采用主成分分析方法对所有变量进行筛选,从中选取若干对产量具有最佳解释能力的新综合变量。结果表明：对与水稻穗头质量相关性比较显著的特征参数作主成分分析后,确定贡献率高达99.02%的第一主成分代替原先的14个特征参数作为新的综合变量；对水稻群体平方米产量的特征参数作主成分分析后,确定了累计贡献率达99.95%的第一、第二主成分代替原来的7个特征参数作为新的综合变量；
6、用多元线性回归方法建立水稻穗头质量、水稻平方米产量的数学模型。建立的穗头质量模型为:Y=5.7174-0.3668z1,式中Y为穗头质量,Z1为表征穗头质量的主成分；建立水稻平方米产量模型为：Y=0.7889+0.0598z1+0.0295z2+0.0541z3,式中Y为每平方米产量,单位kg/m2,Z1、Z2、Z3是水稻平方米产量的主成分。
7、用后验差检验法对模型精度进行验证。后验差检验验证残差分布的统计特性,验证结果为：穗头质量模型精度为一级——优,田间平方米产量的模型精度为三级——勉强合格。
本研究为分形理论、纹理分析在农业工程方面的应用提供一种新的思路和启发。水稻穗头质量模型的建立将为水稻品种的培育研究提供参考依据；平方米水稻产量模型的建立将为水稻产量测量提供一种新的方法,为联合收割机的测产装置提供一种新的选择。
Pre-estimating the yield of grain crops is one of the significant content of the precision agriculture. Currently, many relevant researches have been reported over the world, and so(?)ne pre-estimating approaches have been applied to the practical production. However, most of these methods have the disadvantages of needing many manpower as well as material recourses, and some of them were very unconvinent in collecting basic data, thus it is too difficult to popularize these methods in rural area. Simple, practical and less-investment methods for pre-estimating the yield have been required.
In this paper, author proposed a novel method for estimating the paddy yield on the basis of the fractal theory and the image texture analysis. Presently, traditional on-the-spot sampling and survey methods, remote sensing yield estimating and predicting yield based on the crop-environment model are three main methods. Traditional on-the-spot sampling and survey methods are time and labor consuming and low efficiency. Remote sensing yield estimating needs an enormous input of finacial and material recourses. For the methods based on the crop-environment model, it is very hard to collect the vast amount of meteorological data and agricultural feature parameters. The image texture analysis and the fractal theory have the superiority in describing objects which present abnormities in a microscopic scales but show regularities in a macroscopic scales. In this paper, based on image texture analysis and the fractal theory, feature parameters of mass were extracted from images of individual paddy spikes and paddy plots, the correlativities between these feature parameters and the yields were studied, mathematical models were established to measure the mass of individual paddy spikes and the per-square-meter yields of paddy plots. Finally,the PCA technology was used for precision pre-estimating the yield of grain crops. Main contents and conclusions were summed up as follows:
1. A novel thought and approach was brought foreward for pre-estimating the yield of paddy crops. In this paper, based on the images of individual paddy spikes and paddy plots in their maturation phase, using digital image processing technology, and combining with the fractal theory and the texture analysis, a new method was designed and studied to estimate the yield of paddy grain. This method achieved the aim of simple, practical and less-investment, and provided a theoretical basis for further researches about accurate yield pre-estimating system.
2. Fractal feature parameters of the images of paddy spikes and paddy plots were extracted. The shap of individual paddy spikes and paddy plots present an distinct abnormity in partial areas. Obviously, it is very hard to derive characteristic parameters in a traditional domain of Euclidean geometry. The fractal theory provides us a effective way to extract feature parameters of the images of paddy spikes and paddy plots. In this paper, whether those images bear fractal features were studied, the algorithms of extracting the fractal demention (FD) were worked over based on the definition and the existing calculating principles of the FD, and eventually the FDs were extracted from preprocessed images of paddy spikes and paddy plots using a calculation programme exploited on a VC++ platform. The result shows that the images of paddy spikes and paddy plots bear fractal features. In our researches, calculation programmes were disigned to extract the Box Counting Dimensions (BC) from binorized images, the Differential Box Counting Dimensions (DBC) and the multi-fractal dimensions (D(5)), and relevent feature parameters were extracted.
3. Texture feature parameters of the images of paddy spikes and paddy plots were extracted. The texture of individual paddy spikes and paddy plots present an abnormity in partial areas, but as a whole, it shows a certain regularity. This is the characteristic of the texture. In this paper, based on the description and the statistical methods of texture feature, calculation programmes were designed to extract textural feature parameters. From histogram features, the mean, the variance, the smoothness, the consistency, the third order moment and the entrop of the gray level were extracted. From the gray-level co-occurrence matrix, the diagonal second order moment, the correlation degree, the contrast grade, the entrop, the inverse difference moment and the variance of sum were extracted. And from the gray level-gradient co-occurrence matrix, the energy, the gray average, the gradient average, the correlation degree, the entropy of mixing, the inertia and the inverse difference moment were extracted.
4. The correlativity between the different Box-Counting Dimensions and the textual feature parameters of the images of paddy spikes and paddy plots and the masses of paddy spikes and the per-square-meter yield of paddy plots studied. The result shows that feature parameters which have linear correlativity with the masses of paddy spiked are BC, DBC, texture feature parameters extracted from histogram features (the mean, the variance, the smoothness, the third order moment, the consistency and the entrop of the gray level), the correlation degree and the contrast grade extracted from the gray-level co-occurrence matrix, and thegray average, the gradient average of the gray level-gradient co-occurrence matrix, and those have linear correlativity with the per-square-meter yield of paddy plots are DBC, D(5), the entropy of histogram features, the contrast grade of the gray-level co-occurrence matrix, the gray average and the gradient average of the gray level-gradient co-occurrence matrix.
5. In our research, Principal Component Analysis (PCA, a vector space transform often used to reduce multidimensional data sets to lower dimensions for analysis) were used to extract some aggregate variables which bear best explanatory ability to the yield. Instead of the original variables, fewer new aggregate variables were used in establishing regression models. These models were used to forecast the mass of individual paddy spike and the per-square-meter yields. The result shows that, instead of primary 7 feature parameters, the contribute rate of the first principal component is as high as 92.83%. instead of primary 6 feature parameters, the contribute rate of the first and the second principal components is as high as 97.37%.
6. The multiple linear regression equation method were used in establishing mathematical models for measuring the masses of individual paddy spikes and the per-square-meter yields of paddy plots. The model for measuring the masses of individual paddy spikes could described as:Y=5.7174-0.3668z,, where Y equals the mass of a paddy spike, Z1 equals the principal components. The model for measuring the per-square-meter yields could described as:Y=0.7889+0.0598z1+0.0295z2+0.0541z3, where Y equals the per-square-meter yield, Z1, Z2, Z2 equals the first and the second principal components.
7. The posterior-variance-test was used in model precision grade testing. Results show that the precision grade of the model for measuring the masses of individual paddy spikes isⅠ(excellent). The precision grade of the model for measuring the per-square-meter yields isⅢ(reluctantly qualified).
This research provided a novel idea and inspiration for the application of the fractal theoty and the image texture analysis in agricultural engineering. The model, which was used to measure the mass of individual paddy spike, would give references to the researches of cultivating new paddy varieties. The models of the per-square-meter yield provide a novel approach to measuring the yields of paddy rice, and could give a new choice in designing an estimating device which could be fixed on a combine harvester.
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